undergraduate programs in...

The University of Arizona

Undergraduate Programs

inMathematics

2015–2016

The information and requirements given here apply to the 2015–2016 catalog. For other catalogyears, please consult the archive (http://math.arizona.edu/academics/undergrads/requirements/majors/archive).

This booklet describes the undergraduate degree programs in Mathematics avail-able for a student at The University of Arizona. It also contains information aboutfacilities, activities, jobs, advising, and other services and activities supportive ofthe undergraduate math programs, e.g., what they are, where to find them, whomto contact, and so on.

The contents of this booklet are a subset of the information available at the websitehttp://math.arizona.edu/academics/undergrads and the latest version of thisbooklet, in PDF form, may be downloaded from that web address. You arepresently looking at the booklet created on: December 1, 2015

To request an appointment with an advisor or ask a question, please use thecontact forms at http://math.arizona.edu/academics/undergrads/advising/contact.

Undergraduate ProgramDepartment of MathematicsThe University of Arizona

P.O. Box 210089Tucson, AZ 85721

[email protected]

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Contents

Why study mathematics? 5

Why declare a math major? . . . . . . . . . . . . . . . . . . . . . . . . . 5

More reasons to become a math major . . . . . . . . . . . . . . . . . . . 6

Careers in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Educators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Practitioners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Undergraduate Mathematics Degrees and Requirements 10

Comparing the B.A. and the B.S. . . . . . . . . . . . . . . . . . . . . . . 10

The B.A. in Mathematics . . . . . . . . . . . . . . . . . . . . . . . 10

The B.S. in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . 10

Double Degrees: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

B.A./B.S. in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Core Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Comprehensive Option . . . . . . . . . . . . . . . . . . . . . . . . . 14

Computer Science Option . . . . . . . . . . . . . . . . . . . . . . . 15

Economics or Business Option . . . . . . . . . . . . . . . . . . . . . 16

General/Applied Mathematics Option . . . . . . . . . . . . . . . . . 17

Probability and Statistics Option . . . . . . . . . . . . . . . . . . . 18

Life Sciences Option . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Mathematics Education Option . . . . . . . . . . . . . . . . . . . . 20

Advising, Activities, and Events 21

The Undergraduate Math Majors Advising Center . . . . . . . . . . . . . 21

Faculty Advisors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

College of Science Advising Office . . . . . . . . . . . . . . . . . . . 22

Math Majors Events Calendar . . . . . . . . . . . . . . . . . . . . . . . . 22

3

4

The MathCats Club . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Putnam Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Problem–Solving Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . 23

Undergraduate Research Seminar . . . . . . . . . . . . . . . . . . . . . . 23

Math Colloquia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Undergraduate Colloquium . . . . . . . . . . . . . . . . . . . . . . . 24

Mathematics / Applied Mathematics Colloquium . . . . . . . . . . 24

Math Instruction Colloquium . . . . . . . . . . . . . . . . . . . . . 24

Graduate Student Colloquium . . . . . . . . . . . . . . . . . . . . . 24

Applied Mathematics Brown Bag Colloquium . . . . . . . . . . . . 25

Opportunities for Math Majors 26

Department-level Opportunities . . . . . . . . . . . . . . . . . . . . . . . 26

Undergraduate Research . . . . . . . . . . . . . . . . . . . . . . . . 26

Undergraduate Teaching Opportunities . . . . . . . . . . . . . . . . 26

Tutoring Jobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Honors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

University-level Opportunities . . . . . . . . . . . . . . . . . . . . . . . . 27

Undergraduate Biology Research Program . . . . . . . . . . . . . . 27

UA NASA Space Grant Program . . . . . . . . . . . . . . . . . . . 28

UA Summer Research Institute . . . . . . . . . . . . . . . . . . . . 28

Teaching Teams Program . . . . . . . . . . . . . . . . . . . . . . . . 28

UA Career Services . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Internships and Outside Programs . . . . . . . . . . . . . . . . . . . . . . 28

Internships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Summer Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Semester Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5

Why study mathematics?

In many disciplines, the history of the twentieth century tells of the introductionof more and more mathematical techniques. Mathematics has been establishedas a universal ingredient in the understanding of the world, and is the languageused in conveying this understanding. As we enter the twenty-first century, highermathematics is not just a tool for physical scientists and engineers, but it is alsoof crucial importance in business, economics, and even the social sciences. Manymathematicians still delight in the aesthetic appeal of their subject; however, itis ultimately the application of mathematics that makes it a critical element inmodern civilization.

Why declare a math major?

Undergraduate training in mathematics is an important step along many careerpaths. It is essential for those who intend to continue toward a graduate degree in

More reasons to become a math major 6

Mathematics, Applied Mathematics, Statistics, or Computer Science. Admissionscommittees for graduate studies in Astronomy, Physics, Engineering, Economics,or Finance often prefer students with undergraduate mathematics majors (togetherwith the proper minor) over students who have majored in their own subject. SomeUniversity of Arizona mathematics graduates have also used their degree as the firststep toward professional degrees in law, medicine, and even divinity.

The mathematics major is not just a path toward graduate education. Mathematicstraining is training in general problem solving. Many employers recognize this fact;they also recognize that a Bachelors degree in mathematics is proof of an abilityand willingness to work hard. Many Mathematics majors have found success bycompleting more than one major. Double majors in Mathematics and Science,Mathematics and Business, or even Mathematics and a Social Science, preparegraduates with enhanced ability to compete well in the job market.

Mathematics majors are advised to develop both computing skills and commu-nication skills during their time as a student. Computing skills are increasinglyimportant in today’s society. Experience using graphing calculators and standardmathematical software packages, programming experience, and experience usingthe Internet are extremely useful. And in virtually any type of position, the needfor good communication skills is paramount.

More reasons to become a math major

Let us not forget one of the main reasons for becoming a mathematics major. It isfun! The mathematics program affords students plenty of time to link their math-ematical interests to other intellectual endeavors. Students who combine mathe-matics, computer science, and another area will find themselves with many optionswhen they graduate with an undergraduate degree.

The Department of Mathematics created the Math Center to ensure that our math-ematics majors have a home base to turn to during their undergraduate studies.One of our goals is to integrate the undergraduate mathematics major into theintellectual life of this university and this nation. The working mathematician isinvolved in three areas: the creation of new mathematics, the application of math-ematics to solve real-world problems, and the teaching of mathematics. Many ofour undergraduate mathematics majors are able to perform these same activitiesduring their undergraduate years through various research and teaching/tutoringopportunities and summer internship opportunities.

Careers in Mathematics 7

Careers in Mathematics

There are few jobs with the title Mathematician. Mathematics majors may endup in a job with a title such as Engineer or Analyst. Career opportunities in themathematical sciences fall into two broad categories, Educators and Practitioners:

Educators

University Professor

A Ph.D. degree in mathematics is required for this position. A university profes-sor of mathematics teaches courses, mentors students, and provides service to theinstitution and the community. A university professor can also be considered apractitioner to the extent that he/she conducts research and develops new mathe-matical knowledge. A university professor may also engage in consulting activities.

College Teacher

College mathematics teachers may have a master’s degree or a Ph.D., dependingon the level and nature of the institution. Responsibilities may be exclusivelyinstruction-related, as in the case of a community college, or may include someresearch.

High School or Middle School Teacher

Well-qualified mathematics teachers are in high demand. A bachelor’s degree isthe minumum requirement for teaching in secondary schools. State requirementsfor certification, which usually include courses in education, must also be met.The traditional areas of secondary school mathematics—algebra, geometry, andtrigonometry—have been augmented in many schools by analytic geometry andcalculus and other courses that are intended to meet diverse student needs. Newercurricula include computer programming, probability and statistics, linear algebra,and applications. The prospective teacher who is familiar with these latter areaswill have a competitive advantage.


Practitioners

Actuary

Actuaries are hired by insurance companies (life, health, casualty, etc.), pensionplans, businesses, consulting firms (business and actuarial), and government agen-cies. To become an actuary (Associate or Fellow), one must pass a series of exam-inations administered by the Society of Actuaries. The initial exams are primarilymathematics, including probability and statistics, and can be taken while still anundergraduate student. Because actuarial science is a mixture of mathemetics andbusiness, the student should speak with an advisor about other course work neededto prepare for this career.

Computational Scientist

A computational scientist is an applied mathematician who interprets problemsarising from the physical sciences and engineering in mathematical form and devel-ops mathmatical solutions to these problems. Very large and sophisticated com-puters are used intensively. Potential employers include government laboratories,the chemical industry, and the biotech industry.

Operations Research Analyst

Also called management science analysts, operations research analysts help organi-zations coordinate activities and operate in the most efficient manner, by applyingscientific methods and mathematical principles to organizational problems. Com-puters are used extensively in their work. Students interested in this career pathshould minor in Computer Engineering (COE) or Systems and Industrial Engineer-ing (SIE).

Systems Engineer or Systems Analyst

A systems engineer or analyst usually has substantial course work in engineeringor another technical field. This enables him/her to apply mathematical techniquesto solve the problems unique to the industry of their employer. Students interestedin this career path should consider minoring in Systems and Industrial Engineering(SIE).


Scientific Communication

The scientific publishing industry has a need for scientifically trained individuals forsales and editing. Excellent writing and oral communication skills are essential inthis career field. Accurate and understandable technical writing is widely needed.

Software Engineer or Software Consultant

A software engineer generally designs and writes software that performs nonnumer-ical functions, such as graphics. A background in math and computer science isneeded. Employers include consulting firms and large corporations which do theirown software development. There is also room in this field for the entrepreneur orconsultant.

Statistician

Statistics is both a very applied field and also a theoretical one. Many, but notall, statisticians are active in both applications and the development of new theory,but the greatest potential in terms of jobs is in applied statistics. Statisticiansgenerally work with people in other fields, therefore communication skills are veryimportant. Statistical applications nearly always include the analysis of data andhence some knowledge and experience in computing is very important. There areopportunities for statisticians in the government, in industry, business, medicine,and in academia.

Research Mathematician

In non-academic positions, research mathematicians conduct mathematical researchin areas of interest to large corporations and various departments of government.These include the Department of Energy, various branches of the military, and se-curity agencies. While the demand for non-academic research mathematicians hasbeen shrinking in recent years, there still are positions available at national labo-ratories, the National Security Agency (NSA), and other government entities, aswell as some large corporations. An advanced degree is usually required for thesepositions.

10

Undergraduate MathematicsDegrees and Requirements

The mathematics major is designed to meet many different needs. Our programsallow the student to choose from several options that are each tailored to the indi-vidual’s talents, interests, and career goals. A student may prepare for a variety ofcareers (see p. 7) by selecting the appropriate option and minor. Students choos-ing a mathematics major can take advantage of the full range of mathematicalresources available on campus.

The University offers two different degrees with a major in mathematics, a Bachelorof Arts (B.A.) and a Bachelor of Science (B.S.).

Comparing the B.A. and the B.S.

As far as the mathematics coursework is concerned, the B.A. and B.S. are identical:they each require the core courses (listed on p. 13) and one of seven options (listedon p. 12). The two degrees differ only in the following ways:

• Second language requirement (details below).

• Science/application course requirements (details below).

The B.A. in Mathematics

• Language Requirement: Students must have fourth semester proficiencyin a second language.

• The degree is not science-intensive. Students need to complete only the twoTier One NATS (170) and one Tier Two Natural Science courses, as specifiedin the University General Education requirements (http://gened.arizona.edu/content/information-students).

The B.S. in Mathematics

• Language Requirement: Students must have second semester proficiencyin a second language.

Comparing the B.A. and the B.S. 11

• Laboratory Science Courses Requirement: The degree is science-intensiveand requires one of the following sequences of laboratory science courses:

– PHYS 141 & 142

– PHYS 141 & 241

– PHYS 161H & 162H

– CHEM 151 & 152

– CHEM 105A & 106A & 105B & 106B

– MCB 181R & 181L & ECOL 182R & 182L

– PSIO 201 & 202

– GEOS 251 & 302

– GEOS 251 & 304

• Application Courses Requirement: (This requirement does not apply tothe Mathematics Education Option.) Students must complete at least sixunits of non-math coursework with a prerequisite or corequisite of at leastCalculus I (MATH 122B or higher). Choose from the following: ABE 201,

284, 428, 481A, 481B; ASTR 250, 302; ATMO 421C, 436A, 469A, 469B; BIOC 462A, 462B,

463A, 466; BME 481B; CE 214; CHEE 201, 201L, 202, 301A, 481A, 481B; CHEM 105A,

105B, 404A, 480A, 480B, 481; CSC 345, 422, 433, 436, 437, 445, 453, 460, 477; CSCV 345;

ECE 201R, 381A, 404, 429; ECOL 302, 447, 496N; ECON 332, 361; ENGR 211C, 211P, 265;

GEOG 463; GEOS 322, 342, 356, 419, 432, 434A, 440, 469, 479; HWRS 421, 431, 460A; ISTA

352, 421; MCB 303, 305, 480; MSE 345, 404, 415; OPTI 201R, 221, 404; PHYS 131, 140,

141, 142, 143, 151, 152, 161H, 162H, 240, 241, 251, 261H, 440; PSIO 303A, 303B, 304, 472;

PTYS 407, 411; SIE 250, 265; SWES 305, 420, 470; WSM 402, 460A; or courses approved

by your academic advisor.

Note: B.S. students may satisfy both the Laboratory Science Courses Require-ment and the Application Courses Requirement by completing one of the Physicssequences. The University’s Tier Two General Education Requirement for NaturalScience is satisfied for B.S. students by MATH 313, which is one of the core courses.

Double Degrees:

Students pursuing a second major that has a degree title different from that ofthe first major are technically double degree students. Additional requirementsmay apply to double degree students that do not pertain to double major students(students with two majors that have exactly the same degree title). See an advisorfor detailed information about these additional requirements.

B.A./B.S. in Mathematics 12

B.A./B.S. in Mathematics


Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Mathematicsrequire a core of basic courses (listed on p. 13) followed by additional courses specificto one of seven possible options:

• Comprehensive Option: This option prepares students for graduate study in mathemat-ics, applied mathematics, or most scientific fields. (see p. 14)

• Computer Science Option: This option is for students interested in applications of com-puters to mathematical problems, including math majors who plan to attend graduate schoolin computer science. (see p. 15)

• Economics or Business Option: This option is for students with a particular interestin business applications of mathematics, especially those preparing for graduate school ineconomics or finance. (see p. 16)

• General/Applied Mathematics Option: This option is for students who intend to enterthe job market upon graduation, but may also be appropriate for students who plan to goon to graduate school in a field of science or engineering. (see p. 17)

• Probability and Statistics Option: This option is for students considering a career as anactuary or statistician, as well as for students wanting to attend graduate school in statistics.(see p. 18)

• Life Sciences Option: This option is for students considering a career in medicine, as wellas for students wanting to attend graduate school in the biological sciences. (see p. 19)

• Mathematics Education Option: This option prepares students for teaching mathemat-ics at the secondary school level. The option has two main components: a set of coursesin mathematics, and a set of courses in teaching and learning mathematics in secondaryschools. (see p. 20)

Each option requires at least 15 units of 400-level mathematics course work, andeach option, except Mathematics Education, requires the student to complete aminor. Courses in minors must be distinct from those in the major.

The complete official requirements for each option are given in the University Catalog in the form ofan Academic Advisement Report (ADVIP). Below we cover the portion of the requirements specificto the mathematics major. It is important for students to consult with their academic advisorabout their choice and order of courses, as well as which optional courses would strengthen theirdegree program.


Core Courses


All seven options for the B.A./B.S. require the following core courses, which shouldideally be completed by the end of the sophomore year.

• One of the following programming courses: (1)

– CSC 127A — Introduction to Computer Science

– ISTA 130 — Computational Thinking and Doing

• MATH 122A AND MATH 122B (2) or MATH 125 — Calculus I

• MATH 129 — Calculus II

• MATH 223 — Vector Calculus

• MATH 313 — Introduction to Linear Algebra (3)

• MATH 323 — Formal Mathematical Reasoning and Writing (4)

• MATH 355 — Analysis of Ordinary Differential Equations (5)

(1) Either CSC 127A or ISTA 130 is recommended for most students. Other courses that canbe used to satisfy the programming requirement are: CSC 227, ECE 175, MIS 301, MSE 350, andPHYS 305. These latter courses may require prior programming experience, additional prerequisitesand/or a major or minor declared in another subject.

(2) MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I.They are equivalent to the old MATH 124 course, which is no longer offered.

(3) MATH 313 replaces MATH 215 as of fall semester 2015. Students who completed MATH 215 priorto fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement,though they will not earn upper-division credit for the course.

(4) MATH 323 is a writing-emphasis course that is the foundation for many of the advanced coursestaken by any math major. It should be taken as soon as possible and before most of the 400-levelcourses in the major. Students who do not do well in MATH 323 should speak to an advisor abouttheir choice of major/option.

(5) MATH 355 is the differential equations course that all mathematics majors are expected totake. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticatedapproach to differential equations. MATH 254 is a differential equations course that is aimed atpreparing students for engineering and science applications. Students with an additional major inengineering or science may ask their math faculty advisors for permission to substitute MATH 254course for MATH 355 if a scheduling issue arises.


Comprehensive Option


This option covers the minimum requirements for admission to most graduateprograms in mathematics and applied mathematics. We have separate informa-tion on selecting the appropriate option and courses to prepare for various typesof graduate programs (see http://math.arizona.edu/academics/undergrads/grad-prep).Students selecting the comprehensive option should consult with a MathematicsDepartment faculty advisor in choosing additional course work to ensure that theyare prepared for the graduate school of their choice. A minor in any subject isrequired with this option.

Students completing this option are expected to be proficient in proof writing beforebeginning most of the 400-level courses below. It is recommended that studentswho do not earn an A or B in MATH 323 speak with an advisor about their selectedmath major option before enrolling in proof-intensive 400-level courses.

• Core Courses (listed on p. 13)

• MATH 413 — Linear Algebra

• MATH 424 — Theory of Complex Variables

• MATH 425A — Real Analysis of One Variable

• MATH 425B — Real Analysis of Several Variables

• One of the following two pairs:

1. MATH 415A — Introduction to Abstract Algebra

2. MATH 415B — Second Course in Abstract Algebra

or

1. MATH 454 — Ordinary Differential Equations and Stability Theory

2. MATH 456 — Applied Partial Differential Equations

For an example of how to order your coursework to heed prerequisites and meet all degree require-ments, please consult the sample 4-year plans (http://math.arizona.edu/academics/undergrads/advising/handouts). You will develop an individualized plan in consultation with your facultyadvisor.


Computer Science Option


A minor in computer science (http://www.cs.arizona.edu/undergrad/minors.html) isrequired with this option.


• One of the following three sequences:

1. MATH 415A — Introduction to Abstract Algebra

2. MATH 415B — Second Course in Abstract Algebra

or

1. MATH 464 — Theory of Probability

2. MATH 466 — Theory of Statistics

or

1. MATH 475A — Mathematical Principles of Numerical Analysis

2. MATH 475B — Mathematical Principles of Numerical Analysis

• Two of the following six courses:

– MATH 413 — Linear Algebra

– MATH 443 — Theory of Graphs and Networks

– MATH 445 — Introduction to Cryptography

– MATH 446 — Theory of Numbers

– MATH 447 — Combinatorial Mathematics

– CSC 473 — Automata, Grammars and Languages (*)

• A fifth 400-level course, to be selected with approval from your math faculty advisor.

(*) Students minoring in Computer Science may not double-dip courses with their math major,

beyond their introductory programming course (i.e. CSC 127A). Students with a double major in

Computer Science and Mathematics may be able to double-dip additional courses between the two

majors, within reasonable limits. It is important to consult with both major advisors when planning

your coursework to avoid graduation delays.



Economics or Business Option


This option requires either

• an Economics Minor (http://econ.arizona.edu/undergraduate/minors.asp), or

• a Business Administration Minor (http://ugrad.eller.arizona.edu/academics/minors/business.asp), or

• a Finance Minor (http://www.ugrad.eller.arizona.edu/academics/minors/finance.asp), or

• a Thematic Minor (http://www.registrar.arizona.edu/thematicminor.htm) em-phasizing courses from two or more disciplines/subject areas such as Eco-nomics, Business, and Finance.

The minor should be chosen in consultation with an advisor.

Students completing this option are expected to be proficient in proof writing beforebeginning their 400-level course work. It is recommended that students who do notearn an A or B in MATH 323 speak with an advisor about their selected mathmajor option before enrolling in 400-level courses.



• MATH 464 — Theory of Probability

• Two of the following four courses:


– MATH 425B — Real Analysis of Several Variables

– MATH 466 — Theory of Statistics

– MATH 468 — Applied Stochastic Processes




General/Applied Mathematics Option


A minor in any subject is required with this option.


• MATH 422 — Advanced Applied Mathematics

• MATH 485 — Mathematical Modeling

• One of the following three sequences:

1. MATH 454 — Ordinary Differential Equations and Stability Theory

2. MATH 456 — Applied Partial Differential Equations

or

1. MATH 464 — Theory of Probability

2. MATH 466 — Theory of Statistics

or

1. MATH 475A — Mathematical Principles of Numerical Analysis

2. MATH 475B — Mathematical Principles of Numerical Analysis




Probability and Statistics Option


A minor in any subject is required with this option. Studies in statistics can equipstudents for careers working with data in a wide variety of fields, from biology toeconomics. By discussing with an advisor the choice of the minor, the studentcan greatly enhance his/her career opportunities. Students who are interested inbecoming actuaries will find additional information and suggestions on our Careersin Actuarial Science page (http://math.arizona.edu/academics/undergrads/advising/actuary).

In association with the Graduate Interdisciplinary Program in Statistics, we offer anAccelerated Master’s Program in Statistics. See http://math.arizona.edu/academics/

undergrads/requirements/stats for information.

Students completing this option are expected to be proficient in proof writing beforebeginning their 400-level course work. It is recommended that students who do notearn an A or B in MATH 323 speak with an advisor about their selected mathmajor option before enrolling in 400-level courses.




• MATH 466 — Theory of Statistics

• One of the following two courses:






Life Sciences Option


A minor in the biological sciences is required for this option. Possibilities includeAstrobiology, Biochemistry, Biology, Biosystems Engineering, Ecology & Evolu-tionary Biology, Environmental Sciences, Molecular & Cellular Biology, Physiology,Physiological Sciences, and Pre-Health Professions, or a thematic minor (http://www.registrar.arizona.edu/thematicminor.htm) with a life sciences emphasis. A sec-ond major in a life science area may also be used to fulfill the minor requirement.Courses which may be of interest for your minor include: ECOL 320, 340, 380, 416,426, 453, 496J; MCB 315, 410, 411, 422.


• MATH 422 — Advanced Applied Mathematics


• MATH 485 — Mathematical Modeling


– MATH 310 — Applied Linear Algebra



– MATH 454 — Ordinary Differential Equations and Stability Theory

– MATH 456 — Applied Partial Differential Equations


– MATH 466 — Theory of Statistics




Mathematics Education Option

The information and requirements given here apply to the 2015–2016 catalog. For other catalog years, please consultthe archive (http://math.arizona.edu/academics/undergrads/requirements/majors/archive).

This option is for students preparing to teach mathematics at the secondary school level. The

Education Option has two main components, a set of courses in mathematics, and a set of pedagogy

courses. This option does not require a minor. The Secondary Math Education Program website

(http://math.arizona.edu/~smep/index.html) contains additional information about admission

and requirements.


• Courses in Mathematics:

– MATH 315 — Introduction to Number Theory and Modern Algebra

– MATH 330 — Topics in Geometry

– MATH 361 — Statistics for Teaching

– MATH 404 — History of Mathematics

– MATH 407 — Synthesis of Mathematical Concepts

• Courses in Teaching and Learning Mathematics (Pedagogy):

– MATH 205 — Teaching Secondary Mathematics

– STCH 310 — Adolescent Learning in Science and Mathematics (†)

– SERP 301B — Inclusive Education for Secondary Students With Diverse Abilities

– The following sequence:

1. TLS 416 — An Introduction to Structured English Immersion

2. TLS 417 — Structured English Immersion Methods

– TLS 435 — Content Area Literacy in a Multicultural School

– MATH 406A — Curriculum and Assessment in Secondary School Mathematics

– MATH 406B — Methods of Teaching Mathematics in Secondary Schools

– MATH 494C — Student Teaching

• Constitution Requirement for Arizona State certification — fulfilled by completing one ofthe following: POL 210 or equivalent; a passing score on the AZ and US Constitution exams.

• GPA requirements:

– GPA ≥ 2.5 in MATH 122A&B/125, 129, 223, 313

– Pedagogy GPA ≥ 2.5

– Major GPA ≥ 2.0

– Cumulative UA GPA ≥ 2.0

(†)EDP 301 may be substituted for STCH 310. Contact [email protected] if you need this substitution.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, pleaseconsult the sample 4-year plans (http://math.arizona.edu/academics/undergrads/advising/handouts). You will develop anindividualized plan in consultation with your faculty advisor.

21

Advising, Activities, andEvents

The Undergraduate Math Majors Advising Center

The Undergraduate Math Majors Advising Center, known simply as The Math Cen-ter, supports our undergraduate mathematics degree programs. The Math Centerprovides advising to math majors and minors on course selection and programrequirements. Additionally, we organize events for undergraduates and providefacilities for undergraduate activities including the MathCats student club.

Be sure to watch for a weekly news email from the Math Center ([email protected]) that will announce these and other events that may be of interestto you, as well as important academic announcements that you need to be awareof. It may be helpful to add the Math Center email address to your contacts toensure these messages do not end up in your junk folder. Weekly messages are alsoarchived on our Facebook page (https://www.facebook.com/UAmathmajors).

Faculty Advisors

To help you create a course of study best suited to your talents, interests, andgoals, faculty members from the Mathematics Department have volunteered to actas advisors for math majors.

As students progress in the math major, they are assigned faculty advisors basedon the math major option that has been selected. Your advisor will then - andeach term thereafter - discuss your educational plans with you and help you set upa mathematics program. He or she can provide more helpful information regardingthe content and difficulty level of the specialized 400-level courses that you will betaking. For students who have selected a math major option that has a flexiblefifth 400-level course, the course selection must be approved by the faculty advisor;in fact, he or she will be the one to verify that your math major is complete whenit comes time to graduate.

Your faculty advisor is also a source of information about careers and/or graduateschool, and may know of research and internship opportunities within the Univer-sity and across the country. Each semester, students are sent a message before


priority registration begins to make sure they know who their faculty advisors areand how to reach them.

College of Science Advising Office

The College of Science Advising Office is available for math majors who need tostart their degree checks, are looking for permission to enroll in extra units for asemester, who need their Dean’s permission to withdraw from a course after thedeadline, or if an urgent matter arises and the Undergraduate Program Coordinatoris not available. The College of Science Advising Office is located in the Gould-Simpson Building room 1017. If math is not your primary major, please consultwith your primary college’s advising office for assistance with these issues.

Math Majors Events Calendar

The Math Center maintains a calendar of events of interest to undergraduate mathmajors. Some of these events are put on specifically for math majors – some of themare even organized or sponsored by the Math Center itself. But we also list otherevents that we believe to be of special interest to math majors. The current listingis on the Math Center Events webpage (http://math.arizona.edu/events/ugrads).

The MathCats Club

MathCats is the undergraduate club for students of all majors who are interestedin mathematics. It provides opportunities for students to get to know each other,share experiences, have fun, and help each other succeed.

Putnam Competition

The first Saturday in December, some UA undergraduate students participatein the William Lowell Putnam Mathematical Competition (http://math.scu.edu/putnam/), a national contest sponsored by the Mathematical Association of America(MAA). The competition consists of two 3-hour sessions, during each of which eachstudent individually attempts to solve six problems. The exam is designed to test


originality and creativity in mathematical thinking. The MAA maintains a list oftop participants (http://maa.org/awards/putnam.html) from past competitions.

Problem–Solving Laboratory

The UA Mathematics Problem–Solving Laboratory meets informally once a weekto ponder challenging mathematical problems and learn important techniques forsolving them. A knowledge of calculus is necessary for some problems, but manyproblems require only insight and ingenuity.

All UA undergraduate students are welcome to participate. It is also possibleto register for the seminar as a one-credit pass-fail course, MATH 294A. Formore information, including the meeting place and time for the current semester,see the schedule of classes (http://schedule.arizona.edu). Topics from some pastsemesters can be found on the old MATH 294 website (http://math.arizona.edu/~savitt/teaching/math294/).

Undergraduate Research Seminar

The UA Mathematics Undergraduate Research Seminar, MATH 396C is an excitingopportunity to introduce undergraduates to research and careers in the mathemat-ical sciences. Several different faculty members will present 1-2 lectures each onresearch topics/projects in which undergraduates can become involved. The lec-tures will be given by experts covering computational, mathematical, physical andengineering aspects of the subject accessible to an undergraduate audience. Speak-ers will expose the role of mathematics in the work they do.

The seminar is open to all undergraduates who have completed a course in linearalgebra (MATH 313) or vector calculus (MATH 223). MATH 396C carries one unitof upper-division elective credit, and is generally offered each Spring. This coursemay not be used to fulfill degree requirements for the math major or minor.

Students considering writing an honors thesis in math are encouraged to enrollin the research seminar prior to or during the term in which they will plan theirhonors thesis.

For further information about the seminar, please contact the current URA programcoordinator: [email protected]


Math Colloquia

The School of Mathematical Sciences organizes various colloquia, seminars, andother talks throughout each semester. Whenever such an event is specifically aimedat undergraduate math majors, it is well-publicized and listed on our calendar.However, in general, the colloquia series are always aimed at a wide audience, andundergraduates should consider attending these talks.

Undergraduate Colloquium

On selected afternoons during each semester, the math department organizes hour-long programs designed especially for undergraduate students. Sometimes it is atalk on a mathematical topic by a faculty member or visitor. Sometimes the speakeris a math undergraduate student. Some talks concern an area of mathematics, whileother talks are on practical matters such as careers, graduate school, and selectingupper-division math courses.

Mathematics / Applied Mathematics Colloquium

At least twice a week, talks are presented by distinguished mathematicians fromthe University of Arizona and other institutions around the world. Coffee, tea, andcookies are usually served beforehand. These events provide an opportunity to rubshoulders with faculty members and to see famous mathematicians in action.

Math Instruction Colloquium

This is a colloquium for anyone interested in mathematics education, which in-cludes mathematics undergraduates, graduate students, post-docs, faculty, and lo-cal school teachers. Techniques, strategies, and course content in the teaching ofmathematics are discussed by participants and by leading educators invited fromthe outside.

Graduate Student Colloquium

The math department graduate students organize a weekly colloquium, often ontopics accessible to undergraduate students. The speakers are usually graduate


students presenting aspects of their own research. The atmosphere is generallyrather informal.

Applied Mathematics Brown Bag Colloquium

The graduate students in the Interdisciplinary Program in Applied Mathematicsorganize a weekly colloquium, often on topics accessible to undergraduate students.The speakers are usually graduate students presenting aspects of their own research.The atmosphere is generally rather informal.

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Opportunities for Math Majors

Department-level Opportunities

See http://math.arizona.edu/academics/undergrads/opportunities for de-tails.

Undergraduate Research

Our Undergraduate Research Assistant (URA) program provides opportunities toearn money or credit while engaging in research. You might furthermore have anopportunity to present your research at a conference such as SUnMaRC (http://sunmarc.org/).

Undergraduate Teaching Opportunities

Our Undergraduate Teaching Assistant (UTA) programs provide opportunities toearn money or credit while engaging in teaching-related activites.

Tutoring Jobs

The Center for Recruitment and Retention of Mathematics Teachers (http://crr.math.arizona.edu/) offers an opportunity to observe dynamic teaching, attend tutorpreparation classes for a credit, and tutor middle and high school students for pay.

Other locations on campus that offer tutoring services might also have job oppor-tunities. For a current listing, see the math department tutoring page (http://math.arizona.edu/academics/tutoring).

Honors

Honors Course Work — To graduate with honors from the Honors College, 30 unitsof honors course work are usually required; consult your Honors College advisor formore information.


The Math Department offers a few honors courses/sections that count toward amathematics major, usually at the 100-and 200-level. These honors math coursesare available to highly motivated students with strong mathematical backgrounds.Acceptance to the UA Honors College is not a requirement. Eligibility is determinedbased on what type of student you are: current UA students may be nominatedby the instructor of their current math class; new incoming Freshmen who start atUA in Fall semester may be eligible based on math placement. If you are a newincoming Freshman for Fall semester and would like to know more, please see themath placement advisors at your new student orientation, or contact placement@

math.arizona.edu

In higher-level math courses, students may choose to contract for honors. Juniorsand Seniors in the Honors College may also (with appropriate approvals) take 500-level graduate courses for undergraduate honors credit. Non-honors Seniors withstrong GPAs may also be able to take 500-level courses. Talk to your advisor formore information.

Honors Thesis — To graduate with honors from the Honors College in your majorarea, students need to submit a prospectus outlining their proposed thesis work,and then complete and submit a thesis through the major department. If you areconsidering an honors thesis in mathematics, consult with the Math Center early onfor suggestions to find a project idea and help you connect with a faculty memberto supervise your research. Taking MATH 396C in a spring semester can be a goodway to find a thesis topic and mentor.

University-level Opportunities

There exist many research-related and teaching-related opportunities on the UAcampus. This section lists some of the more prominent of such activities.

The University of Arizona Office of Undergraduate Research website (http://ur.arizona.edu/) can help you find research opportunities around the U of A, and willhelp you connect with projects in your area of interest.

Undergraduate Biology Research Program

To learn more, please visit the Undergraduate Biology Research Program website(http://ubrp.arizona.edu/).


UA NASA Space Grant Program

To learn more, please visit the NASA Space Grant Program website (http://spacegrant.arizona.edu/opportunities/internships/).

UA Summer Research Institute

This program, although run by the UA Graduate College, offers opportunities forundergraduate students. To learn more, please visit the Summer Research Institutewebsite (http://grad.arizona.edu/sri/).

Teaching Teams Program

The primary goal of the Teaching Teams Program (TTP) is to improve learning onthe campus of the University of Arizona. They do this through the creation of aTeaching Team which includes Instructors, Graduate Teaching Assistants (GTAs),and student peer assistants. These student peer assistants are called Preceptors. Tolearn more about becoming a Preceptor, see the Teaching Teams Program website(http://teachingteams.arizona.edu/).

UA Career Services

Besides offering job placement help for current UA students and alumni, UA CareerServices (http://www.career.arizona.edu/) also assists current UA students in findingand landing internships and other career-related experiences. Career counseling,resume reviews, help with interview skills, and assistance with graduate schoolapplications are just a few of the other services they provide.

Internships and Outside Programs

Internships

UA Career Services is the most up-to-date source for information on internshipsavailable to students. They can also help critique your resume, hone your interviewskills, and more. Internships are a great way to gain work-related experience priorto graduation, and in some cases, they have led to offers of permanent jobs for ourstudents after they graduate.


Summer Programs

A wide variety of summer research programs, known as Research Experiences forUndergraduates (or REUs), exist for mathematics majors. Many of these pro-grams not only provide experience that can help students land a job (or graduateschool offer) after graduation, they frequently also pay students to participate!Many of the programs require computer programming experience, so it is recom-mended that students fulfill their math major computer programming requirementearly on in their undergraduate careers. For more information about the types ofprograms available, see our website (http://math.arizona.edu/academics/undergrads/opportunities/external#sum).

Semester Programs

Opportunities also exist for mathematics majors to spend a term studying at an-other institution, either in the United States or abroad. A list of some programswith a strong mathematical focus can be found on our website (http://math.arizona.edu/academics/undergrads/opportunities/external#sem).

For More Information

Contact the Math Center:

[email protected]

http://math.arizona.edu/academics/undergrads/advising/contact

undergraduate programs in...

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